is defined as X = N fm Where m = midpoint of each of the class interval, f = the frequency of each class interval N = ∑ f = total frequency (ii) Short-cut method The arithmetic mean is computed by applying the following formula. X = A + N fd where A is assumed mean (or) arbitrary value, d = m – A is deviations of mid-point from assumed mean and N =∑ f (iii) Step Deviation Method In case of grouped (or) continuous frequency distribution, the arithmetic mean is N fd + c m , where d = m A is any arbitrary value (or) assumed mean and c is the magnitude of class interval. All the above three methods of finding arithmetic mean in continuous case gives us the same answer. Mode: Mode is the value which repeats maximum number of times among the given observations.
Median: Median is exactly a middle value and it exceeds and exceeded by the same number of observations. Median is one of the positional measure. Some other related positional measures are also described below. NOTE It is believed that the students might be familiar with the above concepts and our present syllabus continues from the following.
. . Related Positional Measures - Quartiles, Deciles and Percentiles : Besides median there are other measures which divide a series into equal parts. Important amongest these are quartiles, deciles and percentiles.
- - (i) Quartiles: A measure which divides an array into four equal parts is known as quartiles. Each portion contains equal number of items. The first, second and third points are termed as first quartile ( Q ), second quartile ( Q ) (better named as median) and the third quartile( Q ). The first quartile ( Q ) or lower quartile, has % of the items of the distribution below it and % of the items are greater than it.
Q (median) the second quartile or median has % of the observations above it and % of the observations below it. The upper